Tube Concept for Entangled Stiff Fibers Predicts Their Dynamics in Space and Time

Leitmann, Sebastian; Höfling, Felix; Franosch, Thomas

doi:10.1103/physrevlett.117.097801

Cited by 12 publications

(28 citation statements)

References 53 publications

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“…The seminal tube concept for stiff fibers pioneered by Doi and Edwards [33] furthermore reduces the complex many-body dynamics of such solutions on coarse-grained time and length scales to that of a single needle (phantom needle) with very unusual diffusion coefficients. We have shown recently [26] that this striking simplification is valid for the translation-rotation coupling as well as the intermediate scattering function of the geometric center of the needle.…”

Section: Introductionmentioning

confidence: 92%

“…Information about the spatiotemporal dynamics of the needle center is encoded in the intermediate scattering function (26) with wave vector k and wave number k = |k|. Both integrals extend over all possible initial and final orientations.…”

Section: Intermediate Scattering Function Of the Needlementioning

confidence: 99%

“…As a consequence of this high entanglement, the rotational motion and the translational diffusion perpendicular to the needle slow down drastically, whereas the diffusion along the tube is unaffected. In both theory [15][16][17][18][19][20] and computer simulations [21][22][23][24][25][26] the density-dependent scaling behavior of the long-time rotational and perpendicular translational diffusion coefficients have been established and scale with the number density as n −2 . Computer simulations for two-dimensional toy models have also been performed earlier [27][28][29][30][31] and for a needle in the presence of pointlike obstacles one observes the same scaling laws of the transport coefficients as in three dimensions [29,30].…”

Section: Introductionmentioning

confidence: 99%

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Dynamically crowded solutions of infinitely thin Brownian needles

2017

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We study the dynamics of solutions of infinitely thin needles up to densities deep in the semidilute regime by Brownian dynamics simulations. For high densities, these solutions become strongly entangled and the motion of a needle is essentially restricted to a one-dimensional sliding in a confining tube composed of neighboring needles. From the density-dependent behavior of the orientational and translational diffusion, we extract the long-time transport coefficients and the geometry of the confining tube. The sliding motion within the tube becomes visible in the non-Gaussian parameter of the translational motion as an extended plateau at intermediate times and in the intermediate scattering function as an algebraic decay. This transient dynamic arrest is also corroborated by the local exponent of the mean-square displacements perpendicular to the needle axis. Moreover, the probability distribution of the displacements perpendicular to the needle becomes strongly nonGaussian, rather it displays an exponential distribution for large displacements. On the other hand, based on the analysis of higher-order correlations of the orientation we find that the rotational motion becomes diffusive again for strong confinement. At coarse-grained time and length scales, the spatiotemporal dynamics of the needle for the high entanglement is captured by a single freely diffusing phantom needle with long-time transport coefficients obtained from the needle in solution. The time-dependent dynamics of the phantom needle is also assessed analytically in terms of spheroidal wave functions. The dynamic behavior of the needle in solution is found to be identical to needle Lorentz systems, where a tracer needle explores a quenched disordered array of other needles.

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Section: Introductionmentioning

confidence: 92%

Section: Intermediate Scattering Function Of the Needlementioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Dynamically crowded solutions of infinitely thin Brownian needles

2017

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“…Special cases of the previous equation [Eq. (12)] have already been solved in terms of Mathieu functions for a passive anisotropic Brownian particle (v = 0 and ω = 0) [44], and also for a three dimensional anisotropic passive [45] and active Brownian particle (ω = 0) [41]. Yet, no solution for the ISF of a Brownian circle swimmer has been elaborated up to now.…”

Section: The Modelmentioning

confidence: 99%

Intermediate scattering function of an anisotropic Brownian circle swimmer

Kurzthaler

Franosch

2017

Soft Matter

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Microswimmers exhibit noisy circular motion due to asymmetric propulsion mechanisms, their chiral body shape, or by hydrodynamic couplings in the vicinity of surfaces. Here, we employ the Brownian circle swimmer model and characterize theoretically the dynamics in terms of the directly measurable intermediate scattering function. We derive the associated Fokker-Planck equation for the conditional probabilities and provide an exact solution in terms of generalizations of the Mathieu functions. Different spatiotemporal regimes are identified reflecting the bare translational diffusion at large wavenumbers, the persistent circular motion at intermediate wavenumbers and an enhanced effective diffusion at small wavenumbers. In particular, the circular motion of the particle manifests itself in characteristic oscillations at a plateau of the intermediate scattering function for wavenumbers probing the radius.

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“…Furthermore, the elasticity of a single polymer in free space, as elaborated here, could be used as a reference to study the behavior of a single polymer in crowded environments composed of fixed obstacles [65][66][67], solutions of polymers [68][69][70], or active constituents [8,9,71], as, for example, molecular motors. These give rise to intriguing non-equilibrium physics resembling transport processes inside cells and providing fundamental input for novel active materials [72].…”

Section: Discussionmentioning

confidence: 99%

Elastic behavior of a semiflexible polymer in 3D subject to compression and stretching forces

Kurzthaler

2018

Soft Matter

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We elucidate the elastic behavior of a wormlike chain in 3D under compression and provide exact solutions for the experimentally accessible force-extension relation in terms of generalized spheroidal wave functions. In striking contrast to the classical Euler buckling instability, the force-extension relation of a clamped semiflexible polymer exhibits a smooth crossover from an almost stretched to a buckled configuration. In particular, the associated susceptibility, which measures the strength of the response of the polymer to the applied force, displays a prominent peak in the vicinity of the critical Euler buckling force. For increasing persistence length, the force-extension relation and the susceptibility of semiflexible polymers approach the behavior of a classical rod, whereas thermal fluctuations permit more flexible polymers to resist the applied force. Furthermore, we find that semiflexible polymers confined to 2D can oppose the applied force more strongly than in 3D.

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Tube Concept for Entangled Stiff Fibers Predicts Their Dynamics in Space and Time

Cited by 12 publications

References 53 publications

Dynamically crowded solutions of infinitely thin Brownian needles

Dynamically crowded solutions of infinitely thin Brownian needles

Intermediate scattering function of an anisotropic Brownian circle swimmer

Elastic behavior of a semiflexible polymer in 3D subject to compression and stretching forces

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